Mix the radish wedges, minced shallots, lemon zest, lemon juice, and salt in a bowl. Let sit for 15 to 30 minutes.
Toast the shelled pistachios by heating a small skillet on medium high heat. Add the pistachios and heat until lightly browned. Remove from heat and let cool.
When you are ready to serve, if there is a lot of excess liquid in the radishes, strain some of it out.
Toss the toasted pistachios, mint, and olive oil in with the radishes.
Serve immediately.
